There is complete graph $K_{n}$
Find formula for maksimal number of disjoint to each other $k$-cliques in $K_{n}$. Let denote it as $A(n,k)$
I did some research and i computed a formula: $B(n,k)=\lfloor \frac{{n\choose 2}}{{k\choose 2}}\rfloor$.
I thought that equality $A(n,k)=B(n,k)$ holds for every $n,k$, but i was wrong.
For example:
- $A(4,3)=1=B(4,3)-1$
- $A(5,3)=2=B(5,3)-1$
- $A(6,3)=4=B(6,3)-1$
- $A(6,4)=1=B(6,4)-1$
Is this true that $A(n,k)=B(n,k)-1$?
Regards